PDEA Seminar: Dirac-Bogoliubov-de Gennes equations and applications to inhomogeneous quantum liquids

Abstract: In this talk, I will discuss a pair of coupled PDEs identified as Bogoliubov-de Gennes equations with Dirac operators replacing the usual Laplace ones. The PDEs have spatially-dependent coefficients and can be written in a 2x2-matrix form with non-zero off-diagonal elements arising solely due to spatial inhomogeneities, effectively coupling right- and left-moving degrees of freedom, leading to scattering. I will show how to analytically compute the general Green's functions as well as the scattering matrix encoding how incoming waves scatter to form outgoing ones and how to study their properties. The main physical motivation comes from so-called inhomogeneous Tomonaga-Luttinger liquids, but these PDEs also arise in descriptions of, for instance, superconductor-normal-metal interfaces, polymer chains, and coupled fractional quantum Hall edges.

Participate on site or via Zoom (meeting ID: 67226102216)

This is a seminar in the PDEs and Applications seminar series.